Spatial correlations in chaotic nanoscale systems with spin-orbit coupling Anh Ngo 1 , Eugene Kim 2 and Sergio Ulloa 1 1 Department of Physics and Astronomy, and Nanoscale and Quantum Phenomena Institute, Ohio University, Athens, Ohio. USA. 2 Department of Physics, University of Windsor, Windsor, Ontario, Canada N9B 3P4. Supported by NSF-DMR WMN
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Spatial correlations in chaotic nanoscale systems with spin-orbit coupling
Spatial correlations in chaotic nanoscale systems with spin-orbit coupling. Anh Ngo 1 , Eugene Kim 2 and Sergio Ulloa 1. 1 Department of Physics and Astronomy, and Nanoscale and Quantum Phenomena Institute, Ohio University, Athens, Ohio. USA. - PowerPoint PPT Presentation
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Spatial correlations in chaotic nanoscale systems with spin-orbit coupling
Anh Ngo 1, Eugene Kim2 and Sergio Ulloa 1
1Department of Physics and Astronomy, and Nanoscale and Quantum Phenomena Institute, Ohio University, Athens, Ohio. USA.
2 Department of Physics, University of Windsor, Windsor, Ontario, Canada N9B 3P4.
Supported by NSF-DMR WMN
MotivationsQPC
Vg1
Vg2
J.A. Folk, et al. PRL, 76, 1699 (1996) and A. M. Chang, et al. PRL, 76,1695, (1996).
~
Fluctuations and spatial correlations
of wave functions
Microscopic Model for Chaotic Nanoscale Systems
Random matrix Universal quantities
Theoretical model
Anh Ngo, Eugene Kim and Sergio Ulloa, Submitted (arXiv:1103.3265).
Two point correlation function for up and down spin
The same point in space R=0
Crossover regime
0 1 2 3 4 5 60.0
0.2
0.4
0.6
0.8
1.0
P
Spin-orbit coupling =0.50
P
=1, Up-up spin
=0.18 Up-down spin
0 1 2 3 4 50.0
0.2
0.4
0.6
0.8
1.0
P
P
=0.9 RMT
Spin-orbit coupling =0.10
Spin up and spin downbecome decorrelated
Spin up and spin down
SUMMARY
• We investigate the statistical properties of wave functions in two-dimensional chaotic nanostructures with spin-orbit interactions and magnetic fields.
• Weak spin-orbit coupling is expected to have consequences for spin-polarized tunneling.
• We present results for the evolution of the wave function statistics as a function
of the parameter regimes.
• Numerical calculations for a chaotic stadium billiard are compared with analytic results from random matrix theory.
THANK YOU VERY MUCH !
Spatial correlation of chaotic eigenfunctions
GSE
GOE
One point function
GOE
GUE
General one-point function is for the GOE-GUE crossover
GSE
GOE
GSE
Anh Ngo, Eugene Kim and Sergio Ulloa, Submitted.
GUE
Coral’s wall potential :
Anh Ngo, Eugene Kimand Sergio Ulloa ‘s calculations